I've found that if you wind your coils too tightly, the capacitive reactance will work against the inductance and basically what you have is a trap. When I was experimenting with a vertical antenna for SWL'ing years ago, I wrapped some copper-clad steel antenna wire around a short length of PVC pipe in the middle of two sections of pipe, making a center-loaded vertical. The problem was that it was blocking all signals on the AM BCB. I think it blocked everything 2 MHZ and below. I took a lot of wire off the coil and spread out the turns a bit, and it worked fine.
The problem with a broomstick antenna is that you have so much wire in close proximity to each other, and unless you have a strong signal it's not going to hear very well. It certainly won't hear signals as well as if you took all that wire coiled up on the broomstick and straightened it out. Think of how well you hear signals on a rolled up wire. It just doesn't work that well unless you space out the coils. Something like a stretched-out slinky would work much better.